Answer:
70.4 meters
Step-by-step explanation:
A to B: 40²+10²=c² = 1600+100=c² = 1700=c² = c=√1700 = 41.23
B to C: 25²+15²=c² = 625+225=c² = 850=c² = c=√850 = 29.15
41.23+29.15=70.38
Solution
Let take boat speed = x
Current speed = 4
Upstream = x - 4
Downstream = x + 4
Distance = 9
Time upstream + Time downstream = 10
Time = Distance/Speed
9/(x + 4) + 9/(x - 4) = 10
Solving this equation 9(x-4)+9(x+4) = 10(x^2 -16)
9x - 36 + 9x + 36 = 10x^2 - 160
18x = 10x^2 -160
10x^2 -18x - 160 = 0
Now solving the above quadratic equation, we get
x = 5 or x = -16/5
We ignore the negative value.
The answer is 5.
The speed of the boat in still water is 5mph.
Thank you.
Answer:
All of the symbols don't make this statement true.
Step-by-step explanation:
The absolute value of -1 is 1
The absolute value of 1 is 1
it should be |-1| = |1|
If you can only choose one symbol, my best bet would be >, because 1 can't be greater than 1.
Answer:
<span>y ≤ 0.13x² + 0.38x
</span>y ≤ 766.33 - 2.90x² - 8.69x
Your question doesn't say which are the systems of inequlities, but we can find the correct one.
We can call:
x = width of the grass
y = radius of the dispenser
Now, let's translate into mathematical language the statements given in the question:
- "the length of the grassy area for the lion must be 3 feet greater than its width":
l = x + 3
- "the area of the grass must be at least 8 times greater than the radius of the parakeets' food dispenser":
A ≥ 8 · y
The area of a rectangle is given by:
A = l · w = (x + 3) · x
therefore, we can write the first inequality:
(x + 3) · x ≥ 8 · y
x² + 3x ≥ 8y
and solving for y:
y ≤ 0.13x² + 0.38x (rounded to two decimal digits)
- "The food dispenser for the parakeets is … 4 feet tall. It is exactly half-way full" means that the empty height of the dispenser is:
h = 4 : 2 = 2 ft
- "The cost of the parakeets' food is $0.49 times the length of the radius for every foot of height of food missing from the dispenser":
P = 0.49 · y · h
<span> = 0.49 · y · 2
</span>= 0.98y
- "They could put the grass in the lion's habitat for $2.84 per square foot of grass":
G = 2.84 · A
= 2.84 · (x² + 3x)
= 2.84x² + 8.52x
- "Andrea cannot spend more than $751.00 on both projects":
P + G ≤ 751.00
We can now write the second inequality:
(0.98y) + (2.84x² + 8.52x) ≤ 751.00
Solving for y:
0.98y + 2.84x² + 8.52x ≤ 751.00
0.98y ≤ 751.00 - 2.84x² - 8.52x
y ≤ 766.33 - 2.90x² - 8.69x (rounded to two decimal digits)
.48 is equal to 48/100=12/25 so
28 12/25